User:PAR

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Subjects I'm working on


Help:Displaying a formula

{{note_label|Wood1992||}}

dU=\underbrace{\delta Q}_{\delta Q} + \underbrace{\delta W_{irr}+\delta W_{rev}}_{\delta W}

dU=\underbrace{\delta Q + \delta W_{irr}}_{T\,dS}+\underbrace{\delta W_{rev}}_{-P\,dV}

  • References {{note_label|Wood1992||}} {{ref_harvard|Wood1992|Wood, 1992|}}
  • References reference,,,{{rp|p.103}}
  • References (Harvard with pages)

{{harvnb|Rybicki|Lightman|1979|p=22}}

==References==

{{Reflist|# of columns}}

=== Bibliography ===

{{ref begin}}

*{{Cite book|etc |ref=harv}}

{{ref end}}

  • Template:Cite_web
  • Template:Cite_journal
  • Template:cite book{{cite journal |last1=Herrmann |first1=F. |last2=Würfel |first2=P.|year=2005 |title=Light with nonzero chemical potential |journal=Am. J. Phys |volume=78 |issue=3 |pages=717-721 |publisher=American Association of Physics Teachers |doi=10.1119/1.1904623 |url=https://www.google.com/#hl=en&tbo=d&sclient=psy-ab&q=Herrmann+%22Light+with+nonzero+chemical+potential%22&oq=Herrmann+%22Light+with+nonzero+chemical+potential%22&gs_l=hp.3...227562.227562.1.228017.1.1.0.0.0.0.0.0..0.0.les%3Bcpsugrpq2high..0.0...1.vSu9w3P37vw&pbx=1&bav=on.2,or.r_gc.r_pw.r_qf.&bvm=bv.1355534169,d.eWU&fp=5d1955e51bd5f1c6&bpcl=40096503&biw=1638&bih=807 |accessdate=2012-12-20}} A necessary condition for Planck's law to hold is that the photon number is not conserved, implying that the chemical potential of the photons is zero. While this may be unavoidably true on very long timescales, there are many practical cases that are dealt with by assuming a nonzero chemical potential, which yields an equilibrium distribution which is not Planckian.
  1. History of Wayne, NY
  2. Australian Trilobite Jump table
  3. RGB
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  7. Work7
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  9. Extension to Kummer's test
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  11. Elastic Moduli
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[[Thermodynamics]]

Chi-squared distributions

class="wikitable"

|+

|distribution

|\sigma^2

|\nu

scale-inverse-chi-squared distribution

|\sigma^2

|\nu

inverse-chi-squared distribution 1

|1/\nu

|\nu

inverse-chi-squared distribution 2

|1

|\nu

inverse gamma distribution

|\beta/\alpha

|2\alpha

Levy distribution

|c

|1

Heavy tail distributions

Heavy tail distributions

class="wikitable"
Distribution

|character

|\alpha

Levy skew alpha-stable distribution

|continuous, stable

|0\le \alpha < 2

Cauchy distribution

|continuous, stable

|1

Voigt distribution

|continuous

|1

Levy distribution

|continuous, stable

|1/2

scale-inverse-chi-squared distribution

|continuous

|\nu/2>0

inverse-chi-squared distribution

|continuous

|\nu/2>0

inverse gamma distribution

|continuous

|\alpha>0

Pareto distribution

|continuous

|k>0

Zipf's law

|discrete

|s-1>-1 ???

Zipf-Mandelbrot law

|discrete

|s-1>-1 ???

Zeta distribution

|discrete

|s-1>-1 ???

Student's t-distribution

|continuous

|\nu>0

Yule-Simon distribution

|discrete

|\rho

? distribution

|continuous

|s-1>-1 ???

Log-normal distribution???

|continuous

|\rho

Weibull distribution???

|?

|?

Gamma-exponential distribution???

|?

|?

[[Statistical Mechanics]]

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|+ A Table of Statistical Mechanics Articles

align="center" |

! align="center" |Maxwell Boltzmann

! align="center" |Bose-Einstein

! align="center" |Fermi-Dirac

align="center" |Particle

| align="center" |

| align="center" |Boson

| align="center" |Fermion

align="center" |Statistics

| align="center" colspan=3 |

Partition function

Identical particles#Statistical properties

Statistical ensemble|Microcanonical ensemble | Canonical ensemble | Grand canonical ensemble

align="center" |Statistics

| align="center" |

Maxwell-Boltzmann statistics

Maxwell-Boltzmann distribution

Boltzmann distribution

Derivation of the partition function

Gibbs paradox

| align="center" |Bose-Einstein statistics

| align="center" |Fermi-Dirac statistics

align="center" | Thomas-Fermi
approximation

| align="center" colspan=3 | gas in a box
gas in a harmonic trap

align="center" |Gas

| align="center" |Ideal gas

| align="center" |

Bose gas

Bose-Einstein condensate

Planck's law of black body radiation

| align="center" |

Fermi gas

Fermion condensate

align="center" | Chemical
Equilibrium

| align="center" | Classical Chemical equilibrium

| align="center" colspan=2|

Others:

Continuum mechanics

  • http://online.physics.uiuc.edu/courses/phys598OS/fall04/lectures/

Work pages

To fix:

class="wikitable"
(subtract mean)

|(no subtract mean)

Covariance

|Correlation

Cross covariance

|Cross correlation see [http://astronomy.swin.edu.au/~pbourke/analysis/correlate/ ext]

Autocovariance

|Autocorrelation

Covariance matrix

|Correlation matrix

Estimation of covariance matrices

Proof: Introduce an additional heat reservoir at an arbitrary temperature T0, as well as N cycles with the following property: the j-th such cycle operates between the T0 reservoir and the Tj reservoir, transferring energy dQj to the latter. From the above definition of temperature, the energy extracted from the T0 reservoir by the j-th cycle is

:dQ_{0,j} = T_0 \frac{dQ_j}{T_j} \,\!

Now consider one cycle of the heat engine, accompanied by one cycle of each of the smaller cycles. At the end of this process, each of the N reservoirs have zero net energy loss (since the energy extracted by the engine is replaced by the smaller cycles), and the heat engine has done an amount of work equal to the energy extracted from the T0 reservoir,

:W = \sum_{j=1}^N dQ_{0,j} = T_0 \sum_{j=1}^N \frac{dQ_j}{T_j} \,\!

If this quantity is positive, this process would be a perpetual motion machine of the second kind, which is impossible. Thus,

:\sum_{i=1}^N \frac{dQ_i}{T_i} \le 0 \,\!

Now repeat the above argument for the reverse cycle. The result is

:\sum_{i=1}^N \frac{dQ_i}{T_i} = 0 \,\! (reversible cycles)

In mathematics, it is often desireable to express a functional relationship f(x)\, as a different function, whose argument is the derivative of f , rather than x . If we let y=df/dx  be the argument of this new function, then this new function is written f^\star(y)\, and is called the Legendre transform of the original function.

Category:Wikipedians interested in thermodynamics

PAR

References

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|colspan="3" style="text-align: center;"|Wall (Impermeable)

RigidT-InsNo IWExternal
δQhδWxdTdSdPdVdNdV=0δQh=0δWx=0
Process
    Isobaric process |
|0 |
|0no |
|constant pressure reservoir
    Isochoric process|
|00 |
|yes |
    Isothermal process|
|0 |
|0 |
|no |
|constant temperature reservoir
    Isentropic process00 |
|0 |
|0 |
|yesyes |
    Adiabatic process0 |
|0 |
|yes |
x-Isolated System
    Mechanically Is. (Guha) |
|00yes |
    Adiabatic Is0 |
|0 |
|yes |
    Thermally Is.00 |
|0 |
|0 |
|yesyes |
    Closed system |
|0 |
    Isolated system00 |
|0 |
|00yesyesyes |
    Open system |
|nonono |
Conserved Thermodynamic potential
    U: Internal energy00 |
|0 |
|00yesyesyes |
    F: Helmholtz free energy |
|0 |
|00yesno |
|constant temperature reservoir
    H: Enthalpy00 |
|00 |
|0noyesyesconstant pressure reservoir
    G: Gibbs free energy |
|0 |
|0 |
|0nono |
|constant pressure and temperature reservoir

δQh is heat, δWx is irreversible work, so TdS=δQh+δWx. If both are zero, then dS=0. For the 3 possible walls, "T ins" means thermally insulated, and "No IW" means no irreversible work. "External" specifies the region external to the system.